Since middle ages Ryukyu Kingdom, Amami Oshima have long had faith in such an indigenous folk religion as Noro. This religion maintained sanctuaries such as

The moduli space of spatial polygons is known as a symplectic manifold equipped with both Kähler and real polarizations. In this paper, associated to the Kähler and real polarizations, morphisms of operads 𝖿_𝖪ä𝗁 and 𝖿_𝗋𝖾 are constructed by using the quantum Hilbert spaces ℋ_Käh and ℋ_re, respectively. Moreover, the relationship between the two morphisms of operads 𝖿_𝖪ä𝗁 and 𝖿_𝗋𝖾 is studied and then the equality dim ℋ_Käh = dim ℋ_re is proved in general setting. This operadic framework is regarded as a development of the recurrence relation method by

Abstract : Objective : The presence of accessory root canals, such as furcation canals and lateral branches of the root canal, complicates the pathophysiology of inflammation in the pulp and periodontal tissues, as the accessory root canals may become routes for the transmission of inflammation. In 1972, Simon used a diagram to describe the pathology related to both endodontic and periodontal lesions as endodontic-periodontal lesions. In recent years these lesions have often been categorized into three types. The Type 2 endodontic-periodontal lesion is considered to be caused by periodontal disease with secondary pulpal involvement, but this condition has not been observed in detail. Therefore, this study examined the role of lateral root canals in Type 2 endodontic-periodontal disease in terms of microstructure.

 Materials and Methods : The mandibular right second premolar of a 78-year-old male was extracted because of periodontal disease and observed by micro X-ray CT and scanning electron microscopy.

 Results : Two lateral root canals were seen, at 3.7 mm and 4.5 mm from the root apex. Cementum resorption at the foramina of these branches was apparent, indicating that the periodontal disease had progressed to the foramina. However, fibrous tissue was present within the lateral branches, and no inflammation had invaded the pulp.

 Conclusion : When there is blood circulation from the root apex foramen to the pulp, the lateral branches may resist the progression of inflammation into the pulp, even if the inflammation progresses to the foramina of the lateral canals.

Abstract : Purpose : In Japan, the number of elderly people with many teeth has increased through the 8020 campaign. As a result, there is a growing number of dental diseases that are difficult to treat. Their causative diseases include apical root fracture and cemental tear, but external root resorption is also considered a disease that must be differentiated from other diseases. In this study, external resorption showing a characteristic morphology was observed in the root apex of a mobile molar, and is reported from the viewpoint of its microstructure.

 Case : A 69-year-old male presented to our clinic with a chief complaint of a mobile mandibular right first molar. Treatment consisted of tooth extraction, and observation of the extracted tooth using micro X-ray CT and scanning electron microscopy revealed external root resorption in the mesial root.

 Results and Discussion : In the distal root, there was tartar deposition all the way to the root apex, and a variety of bacteria had formed a biofilm. The shape of the root apical foramen remained and was circular, with a diameter of 0.42 mm. The mesial root had lost surrounding dentin, leaving a root canal, and microstructural observation revealed a shell-shaped resorption fossa and external root resorption of dentin. The structure of the root apical foramen was flat, at 0.12×2.13 mm, and the edges were sharp.

 Conclusion : In teeth in which external resorption of the root apex has occurred, the morphology of the root apical foramen may be altered by the progression of the lesion, making treatment more difficult. Proper treatment and explanation to the patient should be carefully considered.